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My prof noted that if the two components of any ionic compound undergo a large extent reaction with each other, then the substance CANNOT exist as a pure substance.

For example, consider ammonium hydroxide. This is simply ammonia (at least in the solution phase). Can we have a solid, crystalline ammonium hydroxide lattice?

I think this is thermodynamically valid. What about kinetically? Isn't it theoretically possible to have two substances that would otherwise undergo a large extent reaction with each other but don't due to an activation energy barrier?

Are there any such examples?

Also what do you think of the below question?

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Chemistry is a field with far too many exceptions and edge cases to be making sweeping categorical statements. There are numerous examples of ionic compounds that are isolable and stable, the components of which will spontaneously decompose under certain conditions (this is where reaction kinetics is relevant). Two that readily come to mind are ammonium nitrate ($\ce{NH4NO3}$) and ammonium bicarbonate ($\ce{NH4HCO3}$). Both of those can be isolated as pure salts, and both also can and will chemically decompose when circumstances are favorable (the former by multiple possible pathways depending on conditions).

Isn't it theoretically possible to have two substances that would otherwise undergo a large extent reaction with each other but don't due to an activation energy barrier?

This isn't just theoretically possible, it's ubiquitous, it's the norm. If it weren't, human life couldn't exist. Combustion reactions are probably the most obvious and mundane example; just about every organic compound imaginable is usually more thermodynamically stable as a mixture of $\ce{CO2}$, $\ce{H2O}$, $\ce{N2}$, etc., but the kinetic barrier to the reaction (along with physical hindrances and the availability of an oxidizer, e.g., $\ce{O2}$) prevents this from occurring spontaneously without some trigger and the appropriate environmental conditions.

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But ammonium is a weak acid and nitrate anion a base weaker than water. The two don't undergo a "large extent" acid base reaction. So my prof would agree with you that yes, that salt can exist. –  Dissenter Jul 21 at 21:17
    
@Dissenter, if he was talking about this strictly in the context of acid-base reactions, then yes, his point probably has broad validity. –  Greg E. Jul 21 at 21:42
    
@Dissenter, having said that, I should also mention that the situation becomes more complex if we introduce ionic compounds with mixed cations. Ammonium phosphate, for example, is unstable, but ammonium magnesium phosphate forms an extremely stable solid hexahydrate (mineral name struvite). –  Greg E. Jul 21 at 22:02
    
Ah. I'll be sure to hit him over the head with that example. But even in the context of acid-base reactions, can you think of any exceptions? Preferably ones without mixed cations? The ammonium magnesium phosphate one is one for sure. Do you know why exactly that mineral is stable? Does the magnesium cation have anything to do with it? –  Dissenter Jul 21 at 22:13
    
@Dissenter, well, the decomposition of ammonium phosphate is via an acid-base reaction liberating ammonia. In the case of struvite, it forms a hexahydrate, and if I had to hazard a guess, speculatively I'd imagine that ammonium as a hydrogen-bond donor interacts strongly with the oxygen lone pairs. That may be one factor, but I don't know with any certainty. –  Greg E. Jul 21 at 22:25

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